That doesn't actually address my needs and certainly doesn't cater for people who aren't theme developers.

Within the same sidebar, I want to be able to turn off headings for some widgets, but not all. I also want to style some widgets a certain way and some in another way in the same sidebar. And I want to be able to do all this from within the widget admin page, which I think is very possible.

Using widget IDs as per your code gets messed up as soon as I make changes to the widgets, because WordPress may reassign their numbers. Even if not, it requires making CSS changes for every single widget, which is a lot more work than necessary.